A woman fires a rifle with barrel length of 0.5400 m. Let (0, 0) be where the 125 g bullet begins to move, and the bullet travels in the + x-direction. The force exerted by the expanding gas on the bullet is (16,000 + 10,000x - 26,000x2) N, where x is in meters. A) Determine the work done by the gas on the bullet as the bullet travels the length of the barrel.

B) If the barrel is 1.05 m long, how much work is done?

Given that,

Length of barrel = 0.54m

Mass of bullet=125g=0.125kg

Force extend

F=16,000+10,000x-26,000x²

a. Work done is given as

W = ∫Fdx

W = ∫ (16,000+10,000x-26,000x² dx from x=0 to x=0.54m

W=16,000x+10,000x²/2 - 26,000x³/3 from x=0 to x=0.54m

W=16,000x+5,000x² - 8666.667x³ from x=0 to x=0.54m

W = 16,000 (0.54) + 5000 (0.54²) - 8666.667 (0.54³) + 0+0-0

W=8640+1458-1364.69

W=8733.31J

The workdone by the gas on the bullet is 8733.31J

b. Work done is given as

Work done when the length=1.05m

W = ∫Fdx

W = ∫ (16,000+10,000x-26,000x² dx from x=0 to x=1.05m

W=16,000x+10,000x²/2 - 26,000x³/3 from x=0 to x=1.05m

W=16,000x+5,000x² - 8666.667x³ from x=0 to x=1.05mm

W = 16,000 (1.05) + 5000 (1.05²) - 8666.667 (1.05³) + 0+0-0

W=16800+5512.5-10032.75

W=12,279.75J

The workdone by the gas on the bullet is 12,279.75J